Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power

1995 ◽  
Vol 11 (5) ◽  
pp. 1148-1171 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Time Series ◽  
Asymptotic Distribution ◽  
Unit Root ◽  
Convex Combination ◽  
Ordinary Least Squares ◽  
Power Functions ◽  
Large Power ◽  
Unit Root Testing ◽  
Local Asymptotic Power ◽  
Fuller Distribution

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.The paper derives the asymptotic distribution of ordinary least-squares estimates of the largest autoregressive root and its t-statistic. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a convex combination of the Dickey-Fuller distribution and the standard normal, the mixture depending on the correlation between the equation error and the regression covariates. The local asymptotic power functions associated with these test statistics suggest enormous gains over the conventional unit root tests. A simulation study and empirical application illustrate the potential of the new approach.

An Empirical Study on Efficient Market Hypothesis: The Case of Indian Capital Markets

2014 ◽  
Vol 1 (2) ◽  
Author(s):  
Anjala Kalsie
Keyword(s):  
Time Series ◽  
Empirical Study ◽  
Time Series Analysis ◽  
Unit Root ◽  
Weak Form ◽  
Efficient Market Hypothesis ◽  
Efficient Markets ◽  
Test Unit ◽  
Unit Root Testing ◽  
Univariate Time Series

The objective of this paper is to study the efficiency of Indian stock markets during the period 2001-2011. The weak form of efficient markets is extensively tested using NIFTY and 6 major NSE sectoral indices Pharma, IT, MNC, Bank, FMCG and Nifty Junior. Univariate time series analysis of indices returns is carried using tests for randomness / non-stationarity - runs test, unit root testing. ACF, correlograms and other relevant statistical methods. The study concludes that Indian markets are inefficient in its weak form for the study period.

scholarly journals Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown

1994 ◽  
Vol 10 (3-4) ◽  
pp. 672-700 ◽  
Author(s):  
Graham Elliott ◽  
James H. Stock
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Critical Values ◽  
Asymptotic Power ◽  
Time Series Regression ◽  
Second Stage ◽  
Alternative Approach ◽  
Local Asymptotic Power ◽  
Size Distortions ◽  
Correct Size

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.

GLS-BASED UNIT ROOT TESTS WITH MULTIPLE STRUCTURAL BREAKS UNDER BOTH THE NULL AND THE ALTERNATIVE HYPOTHESES

2009 ◽  
Vol 25 (6) ◽  
pp. 1754-1792 ◽  
Author(s):  
Josep Lluís Carrion-i-Silvestre ◽  
Dukpa Kim ◽  
Pierre Perron
Keyword(s):  
Unit Root ◽  
Structural Breaks ◽  
Alternative Hypothesis ◽  
Generalized Least Squares ◽  
Unit Root Tests ◽  
Power Functions ◽  
Trend Function ◽  
Economic Statistics ◽  
Local Asymptotic Power ◽  
Alternative Hypotheses

Perron (1989, Econometrica 57, 1361–1401) introduced unit root tests valid when a break at a known date in the trend function of a time series is present. In particular, they allow a break under both the null and alternative hypotheses and are invariant to the magnitude of the shift in level and/or slope. The subsequent literature devised procedures valid in the case of an unknown break date. However, in doing so most research, in particular the commonly used test of Zivot and Andrews (1992, Journal of Business & Economic Statistics 10, 251–270), assumed that if a break occurs it does so only under the alternative hypothesis of stationarity. This is undesirable for several reasons. Kim and Perron (2009, Journal of Econometrics 148, 1–13) developed a methodology that allows a break at an unknown time under both the null and alternative hypotheses. When a break is present, the limit distribution of the test is the same as in the case of a known break date, allowing increased power while maintaining the correct size. We extend their work in several directions: (1) we allow for an arbitrary number of changes in both the level and slope of the trend function; (2) we adopt the quasi–generalized least squares detrending method advocated by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836) that permits tests that have local asymptotic power functions close to the local asymptotic Gaussian power envelope; (3) we consider a variety of tests, in particular the class of M-tests introduced in Stock (1999, Cointegration, Causality, and Forecasting: A Festschrift for Clive W.J. Granger) and analyzed in Ng and Perron (2001, Econometrica 69, 1519–1554).

scholarly journals UNIT ROOT TESTING IN PRACTICE: DEALING WITH UNCERTAINTY OVER THE TREND AND INITIAL CONDITION

2009 ◽  
Vol 25 (3) ◽  
pp. 587-636 ◽  
Author(s):  
David I. Harvey ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Decision Rule ◽  
Unit Root ◽  
Ordinary Least Squares ◽  
Unit Root Tests ◽  
Trend Detection ◽  
Initial Condition ◽  
Finite Sample ◽  
Testing Procedures ◽  
Unit Root Testing ◽  
Deterministic Trend

In this paper we focus on two major issues that surround testing for a unit root in practice, namely, (i) uncertainty as to whether or not a linear deterministic trend is present in the data and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power properties across such uncertainties. For the first issue, if the initial condition is negligible, quasi-differenced (QD) detrended (demeaned) Dickey–Fuller-type unit root tests are near asymptotically efficient when a deterministic trend is (is not) present in the data generating process. Consequently, we compare a variety of strategies that aim to select the detrended variant when a trend is present, and the demeaned variant otherwise. Based on asymptotic and finite-sample evidence, we recommend a simple union of rejections-based decision rule whereby the unit root null hypothesis is rejected whenever either of the detrended or demeaned unit root tests yields a rejection. Our results show that this approach generally outperforms more sophisticated strategies based on auxiliary methods of trend detection. For the second issue, we again recommend a union of rejections decision rule, rejecting the unit root null if either of the QD or ordinary least squares (OLS) detrended/demeaned Dickey–Fuller-type tests rejects. This procedure is also shown to perform well in practice, simultaneously exploiting the superior power of the QD (OLS) detrended/demeaned test for small (large) initial conditions.

scholarly journals New Estimator for AR (1) Model with Missing Observations

2021 ◽  
Vol 23 (09) ◽  
pp. 147-159
Author(s):  
Mohamed Khalifa Ahmed Issa ◽  
Keyword(s):  
Time Series ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Unit Root ◽  
Constant Term ◽  
Ordinary Least Squares ◽  
Missing Observations ◽  
New Form ◽  
Near Unit Root

In this paper, new form of the parameters of AR(1) with constant term with missing observations has been derived by using Ordinary Least Squares (OLS) method, Also, the properties of OLS estimator are discussed, moreover, an extension of Youssef [18]has been suggested for AR(1) with constant with missing observations. A comparative study between (OLS), Yule-Walker (YW) and modification of the ordinary least squares (MOLS) is considered in the case of stationary and near unit root time series, using Monte Carlo simulation.

Deterministic or Stochastic Trend

Methodology ◽  
2010 ◽  
Vol 6 (2) ◽  
pp. 83-92 ◽  
Author(s):  
Tetiana Stadnytska
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Long Range ◽  
Unit Root ◽  
Stochastic Trend ◽  
Testing Procedures ◽  
Monte Carlo Experiments ◽  
Unit Root Testing ◽  
Stochastic Trends ◽  
Memory Characteristics

Time series with deterministic and stochastic trends possess different memory characteristics and exhibit dissimilar long-range development. Trending series are nonstationary and must be transformed to be stabilized. The choice of correct transformation depends on patterns of nonstationarity in the data. Inappropriate transformations are consequential for subsequent analysis and should be omitted. The objectives of this article are (1) to introduce unit root testing procedures, (2) to evaluate the strategies for distinguishing between stochastic and deterministic alternatives by means of Monte Carlo experiments, and (3) to demonstrate their implementation on empirical examples using SAS for Windows.

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